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Porubov A.V.,Institute of Problems in Mechanical Engineering | Andrianov I.V.,RWTH Aachen | Danishevs'Kyy V.V.,Prydniprovska State Academy of Civil Engineering and Architecture
International Journal of Solids and Structures | Year: 2012

Nonlinear strain wave propagation along the lamina of a periodic two-component composite was studied. A nonlinear model was developed to describe the strain dynamics. The model asymptotically satisfies the boundary conditions between the lamina, in contrast to previously developed models. Our model reduces an initial two-dimensional problem into a single one-dimensional nonlinear governing equation for longitudinal strains in the form of the Boussinesq equation. The width of the lamina may control the propagation of either compression or tensile localized strain waves, independent of the elastic constants of the materials of the composite.© 2012 Elsevier Ltd. All rights reserved. Source


Andrianov I.V.,RWTH Aachen | Danishevs'Kyy V.V.,Prydniprovska State Academy of Civil Engineering and Architecture | Kalamkarov A.L.,Dalhousie University
International Journal of Solids and Structures | Year: 2012

Static and dynamic problems for the elastic plates and membranes periodically perforated by holes of different shapes are solved using the combination of the singular perturbation technique and the multi-scale asymptotic homogenization method. The problems of bending and vibration of perforated plates are considered. Using the asymptotic homogenization method the original boundary-value problems are reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. In the present paper the perforated plates with large holes are considered, and the singular perturbation method is used to solve the pertinent unit cell problems. Matching of limiting solutions for small and large holes using the two-point Padé approximants is also accomplished, and the analytical expressions for the effective stiffnesses of perforated plates with holes of arbitrary sizes are obtained. © 2011 Elsevier Ltd. All rights reserved. Source


Andrianov I.V.,RWTH Aachen | Danishevs'Kyy V.V.,Prydniprovska State Academy of Civil Engineering and Architecture | Kalamkarov A.L.,Dalhousie University
International Journal of Solids and Structures | Year: 2012

Static problems for the elastic plates and rods periodically perforated by small holes of different shapes are solved using the asymptotic approach based on the combination of the asymptotic technique and the multi-scale homogenization method. Using the asymptotic homogenization method the original boundary-value problem is reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. The combination of the perturbation method and the technique of successive approximations is applied for the solution of the unit cell problems. Taking into the account small size of holes the method of perturbation of the shape of the boundary and the Schwarz alternating method are used. The problems of torsion of a rod with perforated cross-section; deflection of the perforated membrane loaded by a normal load; and bending of perforated plates with circular and square holes are considered consecutively. The error of the applied asymptotic techniques is estimated and the high accuracy of the obtained solutions is demonstrated. © 2011 Elsevier Ltd. All rights reserved. Source


Andrianov I.V.,RWTH Aachen | Danishevs'Kyy V.V.,Prydniprovska State Academy of Civil Engineering and Architecture | Kalamkarov A.L.,Dalhousie University
Composites Part B: Engineering | Year: 2010

The analytical interpolation formulas for the effective electrical conductivity of fiber-reinforced and particulate composites for any volume fractions of inclusions are derived in the present paper. The Garnett formulas are used for a limiting case of small volume fractions of inclusions. And the formulas based on the Shklovskii-De Gennes model are adopted for a limiting case of large volume fractions of inclusions approaching the percolation threshold. The derivation is based on application of the method of asymptotically equivalent functions. This approach presents a natural generalization of the two-point Padé approximants to the case, when in one of the limits the interpolated function cannot be represented in the form of power series. The application of this interpolation technique made it possible to derive the formulas for the effective conductivity of fiber-reinforced and particulate composites with very high volume fractions of inclusions, up to the percolation threshold. The numerical results are compared with the known asymptotic expressions, and also with the existing exact expressions in some limiting cases, for example, in the case of statistically equivalent arrangement of the constituent materials. Comparison with the experimental data confirms the satisfactory accuracy of the obtained analytical results. © 2010 Elsevier Ltd. Source


Karasev A.G.,Prydniprovska State Academy of Civil Engineering and Architecture
Mathematics and Mechanics of Solids | Year: 2014

The influence of periodical imperfections on the buckling load value of shallow elastic closed conical shells undergoing external pressure was investigated by numerical analysis. Results are compared with experimental data. It is established that initial imperfections significantly influence the buckling pressure value only for large imperfection amplitude (an order of magnitude more than the shell thickness). The existence is established of the effect of a 'static resonance'. © The Author(s) 2014. Source

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